12 Volt vacuum pump problem

where did that diagram come from? the only check valve that's drawn correctly is labeled "new check valve"
the instructions dont show any check valves.
IMO there should only be one check valve, the one built into the booster and possibly one between the pump and the pressure switch if it is used with canister(s).
where is the line out of the second canister and where is it connected?
IMO the clue is engine off or running, not a voltage or heat issue.
Are you connected to the pump inlet? (the smaller pipe)
Is the engine vacuum also connected to this system??
unless the motor is faulty, don't think this should be this hard.
Again, try connecting vacuum pump directly to the booster.